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°á¸öµÊ×ÓÀ´,¿´¿´´óÅ£ÈçºÎ½â¾öÕâ¸öÎÒ¾õµÃ³¬ÄѵÄÌâÄ¿.

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Æä´Î,»ý·Ö¶ÔÈ«Æ½Ãæ, »ý·Öº¯ÊýΪ exp(-a* sqrt(x^2+y^2) ) dx dy,
תΪ¼«×ø±ê dx dy = r dr d theta. ¶Ôtheta»ý·ÖµÃµ½ 2 pi, ¶Ô r »ý·ÖΪ
r*exp(-ar) dr ´ÓÁãµ½ÎÞÇî´ó, µÃµ½ a^{-2}. Òò´ËÕû¸ö»ý·ÖΪ 2 pi / a^2.

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°á¸öµÊ×ÓÀ´,¿´¿´´óÅ£ÈçºÎ½â¾öÕâ¸öÎÒ¾õµÃ³¬ÄѵÄÌâÄ¿.

Õâ¸ö¼¶ÊýÏ൱ÓÚ¶Ô¸´Æ½ÃæÉÏËùÓÐÕûµãm+niÇóºÍ sum_z exp(-a* |z|).

Èç¹û²»ÒªÇóClosed Form,¿ÉÒÔÇóÊýÖµ½â,ÓÃÈí¼þ¶Ô¾ßÌåµÄa.
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3Â¥: Originally posted by hank612 at 2013-07-17 10:58:55
Èç¹ûÄãÖ»ÏëÒª¶¨ÐԵĽá¹û,¿ÉÒԲο¼ÇóºÍת»»Îª»ý·Ö.

Ê×ÏÈ,°Ñm nÇóºÍ´ÓÁãµ½ÎÞÇî´ó¸ÄΪ´Ó¸ºÎÞÇî´óµ½ÎÞÇî´ó, ×Ô¼ºËã³öËüÃǵĹØÏµ.

Æä´Î,»ý·Ö¶ÔÈ«Æ½Ãæ, »ý·Öº¯ÊýΪ exp(-a* sqrt(x^2+y^2) ) dx dy,
תΪ¼«×ø±ê dx ...

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